using Imsl.Chart2D;
using Imsl.Stat;
using System.Drawing;

public class SampleProbability : FrameChart {

    public SampleProbability() {
        Chart chart = this.Chart;
        AxisXY axis = new AxisXY(chart);

        double[] ticks = {0.001, 0.005, 0.01, 0.02, 0.05, 0.10, 0.20, 0.30,
            0.40, 0.50, 0.60, 0.70, 0.80, 0.90, 0.95, 0.98, 0.99, 0.995, 0.999};
        double a = ticks[0];
        double b = ticks[ticks.Length-1];

        axis.AxisX.AxisTitle.SetTitle("x");
        axis.AxisY.AxisTitle.SetTitle("Probability");

        axis.AxisY.Transform = Axis.TRANSFORM_CUSTOM;
        axis.AxisY.CustomTransform = new NormalTransform();
        axis.AxisY.AutoscaleInput = Axis.AUTOSCALE_OFF;
        axis.AxisY.SetWindow(a, b);
        axis.AxisY.TextFormat = "0.000";
        axis.AxisY.SetTicks(ticks);
        axis.AxisY.MinorTick.IsVisible = false;

        int nSamples = 400;
        int nBins = 20;

        // Setup the bins
        double[] bins = new double[nBins];
        double dx = 6.0/nBins;
        double[] x = new double[nBins];
        for (int k = 0; k < x.Length; k++) {
            x[k] = -3.0 + (k+0.5)*dx;
        }

        // Generate random normal deviates and sort into bins
        Random r = new Random(123457);
        for (int k = 0; k < nSamples; k++) {
            double t = r.NextNormal();
            int j = (int)System.Math.Round((t+3.0-0.5*dx)/dx);
            if (j <= 0) {
                bins[0]++;
            } else if (j >= nBins-1) {
                bins[nBins-1]++;
            } else {
                bins[j]++;
            }
        }

        // Compute the cumulative distribution
        // y[k] is the sum of bins[j] for j=0,...,k divided by the nSamples.
        double[] y = new double[nBins];
        y[0] = bins[0]/nSamples;
        for (int k = 1; k < nBins; k++) {
            y[k] = y[k-1] + bins[k]/nSamples;
        }

        // Plot the data using markers
        Data data = new Data(axis, x, y);
        data.DataType = Data.DATA_TYPE_MARKER;
        data.MarkerType = Data.MARKER_TYPE_FILLED_CIRCLE;
        data.MarkerColor = Color.Blue;

    }

    public static void Main(string[] argv) {
        System.Windows.Forms.Application.Run(new SampleProbability());
    }
}

class NormalTransform : Transform {
    private double scaleA, scaleB;

    // Initializes the mappings between user and coordinate space.
    public void SetupMapping(Axis1D axis1d) {
        double[] w = axis1d.GetWindow();
        double t = Cdf.InverseNormal(w[0]);
        scaleB = 1.0 / (Cdf.InverseNormal(w[1]) - t);
        scaleA = -scaleB * t;
    }

    // Maps a point in [0,1] to a probability.
    public double MapUnitToUser(double unit) {
        return Cdf.Normal((unit - scaleA) / scaleB);
    }

    // Maps a probablity to the interval [0,1].
    public double MapUserToUnit(double p) {
        return scaleA + scaleB * Cdf.InverseNormal(p);
    }
}